LibreOffice understands both MS Office .doc and .docx formats so you should have no problems importing Word 2003 documents into LibreOffice Writer. In my experience (5 years of using StarOffice then OpenOffice now LibreOffice in both an office and home environment), LibreOffice has rarely had an issue converting an MS Word document properly including formatting. In fact, we have often used LibreOffice to import corrupt MS Word docs that will no longer open in Word, just to repair them.

Whilst the default file format for LibreOffice Writer is .odt, there is nothing to stop you from saving in either .doc or .docx formats if you need to share files with MS Office users. In fact, if you want, you can make one of these formats the default format for saving files (Tools > Options > Load/Save > General > Default file format and ODF settings).

Scripting
Support for macros written in MS Office's VBA is currently extremely limited (and improved support is one of the frequent requests in the user community) so, if you rely on macros then you may have issues converting them manually. LibreOffice's own version of macro scripting is very different and takes some time to get used to.

Java
Some features of LibreOffice require a Java environment, e.g. some Writer Wizards won't work (Letter, Fax, Agenda and Web Page) without Java (SE 6 or 7) or a JRE installed (1.6 or 1.7) as these haven't been developed much since the days of StarOffice when Java was used far more. I believe Writer's MailMerge, LibreOffice Base (especially) and some of the Accessibility tools also require Java. You still appear to need to point LibreOffice to the Java/JRE installation manually (Tools > Options > Advanced > Java options) by selecting which version of Java or JRE is installed.